Correct, all Hindu civs can since version 0.5.0.
No. There's a general rule that far away civs won't vassalize. This only takes starting location into consideration, so may look awkward in Domination games. I can change that in the future patch, so that sharing borders overrides this. Currently the only workaround is capitulation, which ignores distance.
I don't think that Mughals can though.
Good to know. Similarly to DoC, a tech like Compass, that allows ocean trading, could also remove the vassalisation limit, but sharing borders sounds even better.
Btw, the domination victories for Hindu civs are really annoying, because you have to work really hard for not to accindently win the URV, which is ridiciously easy. I usually go around it by spreading other religions for piety loss.